Exploring Angle Sums Using Half Turns

In this investigation, you will explore the sum of the measures of the interior angles of triangles, quadrilaterals and other polygons using rotations of 180° about a midpoint of a side.

Instructions

1. Choose a shape such as a triangle and use the vertices to reshape it as desired.
2. Click near a midpoint of some segment.
3. Repeat step 2 for other midpoints.
4. What does your resulting figure suggest about the sum of the measures of the interior angles for the polygon you have chosen?
5. What happens to the angle sum as you reshape the polygon by moving the original vertices?

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Now try another shape. Do your results stay the same? Explain.